Hausdorff ultrafilters
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- by Mauro Di Nasso and Marco Forti PDF
- Proc. Amer. Math. Soc. 134 (2006), 1809-1818 Request permission
Abstract:
We give the name Hausdorff to those ultrafilters that provide ultrapowers whose natural topology ($S$-topology) is Hausdorff, e.g. selective ultrafilters are Hausdorff. Here we give necessary and sufficient conditions for product ultrafilters to be Hausdorff. Moreover we show that no regular ultrafilter over the “small” uncountable cardinal $\mathfrak {u}$ can be Hausdorff. ($\mathfrak {u}$ is the least size of an ultrafilter basis on $\omega$.) We focus on countably incomplete ultrafilters, but our main results also hold for $\kappa$-complete ultrafilters.References
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Additional Information
- Mauro Di Nasso
- Affiliation: Dipartimento di Matematica “L. Tonelli”, Università di Pisa, Italy
- MR Author ID: 610241
- Email: dinasso@dm.unipi.it
- Marco Forti
- Affiliation: Dipartimento di Matematica Applicata “U. Dini”, Università di Pisa, Italy
- Email: forti@dma.unipi.it
- Received by editor(s): November 24, 2003
- Received by editor(s) in revised form: May 12, 2004
- Published electronically: January 4, 2006
- Additional Notes: This work was partially supported by the MIUR PRIN Grant “Metodi logici nello studio di strutture geometriche, topologiche e insiemistiche”, Italy.
- Communicated by: Alan Dow
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1809-1818
- MSC (2000): Primary 03E05, 03H05, 54D80
- DOI: https://doi.org/10.1090/S0002-9939-06-08433-4
- MathSciNet review: 2207497